A pump of the above type is disclosed in DE 196 18 452 A1. This fuel pump operates satisfactorily when the fuel tank is full but when the tank is almost empty and the fuel level drops below the outlet of the vent valve, a temporary delay in pumping the fuel takes place when the fuel pump is reactivated. This is due to the emptying of the chamber in the casing of the fuel pump when the pump is deactivated until the pump is once again filled after it has been reactivated. This can lead to problems in starting the internal combustion engine.